Stauduhar's Conjecture is stated as Problem 7 in a list of 114 problems, which, according to a
nice tradition of the time, appeared in the Proceedings of
the 1963 Number Theory Conference [1]}.
In several later articles, various authors referred to the same problem, but in the formulation of
R. K. Guy [2]}.
There, Guy draws attention to the phenomenon that the sequence of factorials
\(1!, 2!,\dots ,p!\)  misses about \(p/e\)  residue classes modulo \(p\) .
The conjecture remains unsolved, but it was proved [3]} that it holds in
average for all modular mappings or, in other words,
this is a characteristic of randomly chosen sequences of \(p\)  classes of residues modulo \(p\) .
The link with the 'randomness' was made earlier, as we have found in the last stage of the
preparation of this manuscript. Thus, Brillhart [1]}
adds a comment to the statement of the conjecture, saying in parentheses that
“from extensive numerical calculation
the statement appears to be true” and 'this is the “random result” for any set of
numbers'.
